Moving Finger in blender Moves the other part of hand?
The problem has to do with the vertex groups the bones influence.  

When you parented your mesh to your armature blender created a vertex group on the child mesh for every bone in the armature.  Looking at the bone names you can see the bone with the problem is named "Bone_L.009".  You'll find the corresponding vertex group here:



Select the "Bone_L.009" vertex group and go into Weight Paint mode. 



The problem is pretty obvious: the bone has influence on other parts of the mesh than the intended "finger" (you can see that there is a green area also on the other "finger", thus it is influenced by the same bone).

To correct, in the weight paint brush options set the Weight to 0 and then paint over the problem area of the mesh. 



It should look something like this where you're done:



The fingers will now move independently.